## One Citation

Estimation of the number of negative eigenvalues of magnetic Schr\"odinger operators in a strip

- Physics
- 2021

An upper estimate for the number of negative eigenvalues below the essential spectrum for the magnetic Schrödinger operator with Aharonov-Bohm magnetic field in a strip is obtained. Its further shown…

## References

SHOWING 1-10 OF 22 REFERENCES

Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

- Mathematics
- 2011

We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail…

Eigenvalue bounds for radial magnetic bottles on the disk

- MathematicsAsymptot. Anal.
- 2012

An upper bound on the number of eigenvalues of H smaller than any positive value is obtained, which involves the minimum of B and the square of the L^2 -norm of A( r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centerde in the origin.

Magnetic Dirichlet Laplacian with radially symmetric magnetic field

- Mathematics
- 2016

The aim of the paper is to derive spectral estimates on the eigenvalue moments of the magnetic Dirichlet Laplacian defined on the two-dimensional disk with a radially symmetric magnetic field.

Semiclassical bounds in magnetic bottles

- Mathematics
- 2015

The aim of the paper is to derive spectral estimates into several classes of magnetic systems. They include three-dimensional regions with Dirichlet boundary as well as a particle in $\mathbb{R}^3$…

Gaussian decay of the magnetic eigenfunctions

- Physics, Mathematics
- 1996

We investigate whether the eigenfunctions of the two-dimensional magnetic Schrödinger operator have a Gaussian decay of type exp(−Cx2) at infinity (the magnetic field is rotationally symmetric). We…

Sharp Lieb-Thirring inequalities in high dimensions

- Mathematics
- 1999

We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$…

Bound states in one and two spatial dimensions

- Mathematics, Physics
- 2003

In this article we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive…

On the Lieb-Thirring constantsLγ,1 for γ≧1/2

- Mathematics
- 1995

AbstractLetEi(H) denote the negative eigenvalues of the one-dimensional Schrödinger operatorHu≔−u″−Vu,V≧0, onL2(∝). We prove the inequality(1)
$$\mathop \sum \limits_i |E_i (H)|^{ \gamma } \leqq…

The Stability of Matter in Quantum Mechanics

- Physics
- 2009

Preface 1. Prologue 2. Introduction to elementary quantum mechanics and stability of the first kind 3. Many-particle systems and stability of the second kind 4. Lieb-Thirring and related inequalities…

The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem (代数解析学の最近の発展)

- Mathematics
- 1979

If N ((Ω,λ) is the number of eigenvalues of -Δ in a domain Ω, in a suitable Riemannian manifold of dimension n, we derive bounds of the form \(\tilde N(\Omega ,\lambda ) \le {D_n}{\lambda…